A Priori Constraint and Outlier Suppression Based Image Deblurring Method

ABSTRACT

Provided is an a priori constraint and outlier suppression based image deblurring method. A convolution model is used for fitting a blurring process of a clear image and the blurred image I is restored, so that the purpose of image deblurring is achieved. The method comprises an evaluation process of the significant structure of a blurred image, a process of blurring kernel estimation and outlier suppression, and a process of restoring the blurred image by non-blind deconvolution. A structure in the blurred image is obtained by use of L0 norm constraint and heavy-tailed a priori information. The L0 norm constraint is used to evaluate the blurring kernel. The evaluated blurring kernel is subjected to outlier suppression. The final restored image is obtained by using a non-blind deconvolution algorithm. The present invention can prominently improve the restoration level of the blurred image.

TECHNICAL FIELD

The present invention relates to a digital image processing technology,and more particularly relates to a priori constraint and outliersuppression based image deblurring method.

BACKGROUND ART

A deblurring technology is a theme widely studied in an image and videoprocessing field. In a certain sense, blur caused by camera shakeseriously affects imaging quality and visual perception of an image. Asan extremely important branch of an image preprocessing field,improvement of the deblurring technology directly affects performance ofother computer vision algorithms, such as foreground segmentation,object detection and behavioral analysis. Meanwhile, the improvementalso affects encoding performance of the image. Therefore, thedevelopment of a high-performance deblurring algorithm has an importantrole.

In general, a convolution model can be used for explaining blurringcauses, and a camera shape process can be mapped to a blurring kerneltrajectory PSP (Point Spread Function). A problem of restoring a clearimage when the blurring kernel is unknown belongs to an ill-posedproblem. Therefore, in a usual sense, the blurring kernel should beusually estimated, and then, convolution operation is conducted with theevaluated blurring kernel to obtain a restored image. Currently, commonalgorithms include an MAP-based EM algorithm. In many cases, an originalMAP_(x,k) (wherein x indicates the clear image, k indicates the blurringkernel) algorithm would take the blurred image as no-blur explanation,which makes failure of successive iterative processes of the evaluatedimage and the blurring kernel; and the later MAP_(k) (k indicates theblurring kernel) algorithm is an improvement of MAP_(x,k), which solvesthe problem of the no-blur explanation. This algorithm firstly estimatesthe blurring kernel, and then, the image is restored with non-blinddeconvolution. However, the algorithms have problems that a prioriconstraint is insufficient or inappropriate, and meanwhile, theevaluated blurring kernel has a problem of outlier, which is also notsolved well. This subtle difference may cause the failure of thedeblurring process.

To sum up, the existing deblurring algorithms have disadvantagesincluding that: (I) a priori assumption is incorrect; (II) a prioriconstraint is inappropriate; and (III) the outlier existing in theblurring kernel is not suppressed. This is because the camera shakeprocess is continuous, which decides the continuity of the blurringkernel trajectory. Therefore, the outlier existing in the blurringkernel is bound to cause the failure of a deconvolution process.

SUMMARY OF THE INVENTION

To overcome the disadvantages of the prior art, the present inventionproposes a priori constraint and outlier suppression based imagedeblurring method, which solves the problems of the existing algorithms:a priori assumption is incorrect; a priori constraint is inappropriate;and the blurring kernel has outliers. By solving the problems, thepresent invention can prominently improve the restoration level of theblurred image.

The principle of the present invention is: a priori constraint andoutlier suppression based image deblurring method is proposed to solvethe problems of the existing algorithms: a priori assumption isincorrect; a priori constraint is inappropriate; and the blurring kernelhas outliers. Specifically, based on a MAPk algorithm thought, the apriori constraint and the outlier suppression, image deblurring isrealized. Firstly, a significant structure in the blurred image isobtained by use of L0 norm constraint and heavy-tailed a prioriinformation; secondly, based on the significant structure, the L0 normconstraint is used to evaluate the blurring kernel; then, the evaluatedblurring kernel is subjected to outlier suppression; and finally, thefinal restored image is obtained by using a non-blind deconvolutionalgorithm. The method of the present invention can effectively improvethe restoration of the blurred image by solving the problems of theexisting algorithms: a priori assumption is incorrect; a prioriconstraint is inappropriate; and the blurring kernel has outliers.

The present invention provides the technical solutions:

A priori constraint and outlier suppression based image deblurringmethod is provided. A convolution model is used for fitting a blurringprocess of a clear image, including evaluation of a significantstructure of a blurred image, blurring kernel estimation and outliersuppression, and a restoration process of a non-blind deconvolutionblurred image;

1) An evaluation process of the significant structure of the blurredimage specifically includes the following steps:

11) fitting a blurring process of a clear image by using the convolutionmodel in Formula 1:

I=L⊗k+η  (Formula 1)

wherein I indicates the blurred image, k indicates the blurring kernel,and η indicates the noise (the distribution thereof is assumed to beGaussian noise);

a priori constraint with a heavy-tailed effect is taken as distributionof a significant structure gradient of the blurred image, as shown inFormula 2:

$\begin{matrix}{{\min\limits_{s}{{{S \otimes k} - L}}^{2}} + {\lambda_{1}{{\nabla S}}^{0.5}}} & \left( {{Formula}\mspace{14mu} 2} \right)\end{matrix}$

wherein S indicates the significant structure of the blurred image (notimage to be restored), and is used for evaluating the blurred kernel kin auxiliary manner; the first item of the Formula 2 can be taken as aloss function (which would cause the value increase of the Formula 2,but the present invention evaluates to make an optimized equation reachthe minimum value S; therefore, an optimization process is notaffected); and the second item of the Formula 2 simulates the hheavy-tailed effect with Hyper-Laplacian;

12) evaluating the significant structure of the blurred image:

introducing L0 norm to constrain a texture of the significant structureS of the blurred image, and meanwhile, limiting noise of a smooth regionin S with L2 norm. The updated formula is shown in Formula 3:

$\begin{matrix}{{\min\limits_{s}{{{S \otimes k} - L}}^{2}} + {\lambda_{1}{{\nabla S}}^{0.5}} + {\lambda_{2}{{{\nabla S} \circ M}}_{0}} + {\lambda_{3}{{{\nabla S} \circ \left( {1 - M} \right)}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 3} \right)\end{matrix}$

wherein M indicates two-value calibration of the texture in thesignificant structure S of the blurred image, (1−M) indicates two-valuecalibration of the smooth region in S; and the latter two items (i.e.,the third item and the last item) of the Formula 3 are used for textureconstraint, wherein the third item constrains the details of a largesize, and the last item constrains the smoothness;

M is defined with Formula 4 and Formula 5:

$\begin{matrix}{{r(x)} = \frac{{\sum\limits_{y \in {N_{h}{(x)}}}{\nabla{S(y)}}}}{{\sum\limits_{y \in {N_{h}{(x)}}}{{\nabla{S(y)}}}} + 0.5}} & \left( {{Formula}\mspace{14mu} 4} \right) \\{M = {H\left( {r - \tau_{r}} \right)}} & \left( {{Formula}\mspace{14mu} 5} \right)\end{matrix}$

In the Formula 4, x indicates a location of a pixel point, y indicates apixel point centering on the pixel point and having a window size withina range of N_(h), and r(x) indicates a degree that the pixel point atthe location x belongs to the texture part. The texture in S can bepreliminarily divided with the Formula 4, the value of r(x) is (0, 1),and r(x) is in proportion to the possibility that x belongs to thetexture part. Meanwhile, the Formula 4 also limits the appearance of amutational texture (when the size of the blurring kernel is greater thanthat of the blurred image detail, the image restoration is failed,therefore, the mutational texture should be limited). M in the Formula 5is obtained by Heaviside step function, wherein τ_(r) indicates athreshold of the degree r(x) that the pixel point belongs to the texturepart, which is used for distinguishing a texture region and the smoothregion in the significant structure S. In the present invention, weobtain τ_(r) with a histogram equalization method;

13) solving the significant structure of the blurred image, specificallyas follows:

Introducing two substitution variables u and w to selectively substitute∇S to solve the Formula 3, and updating S with an iterative method. Avariant of the Formula 3 is as follows:

$\begin{matrix}{{\min\limits_{S,u,w}{{{S \otimes k} - L}}^{2}} + {\lambda_{1}{w}^{0.5}} + {\lambda_{2}{{u \circ M}}_{0}} + {\lambda_{3}{{u \circ \left( {1 - M} \right)}}_{2}^{2}} + {\beta{{u - {\nabla S}}}_{2}^{2}} + {\gamma{{w - {\nabla S}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 6} \right)\end{matrix}$

We obtain the solution of each iteration S, u and w with alternatelyupdated method; Solution of the variable u:

$\begin{matrix}{{\min\limits_{u}{\lambda_{2}{{u \circ M}}_{0}}} + {\lambda_{3}{{u \circ \left( {1 - M} \right)}}_{2}^{2}} + {\beta{{u - {\nabla S}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 7} \right) \\{u = \left\{ \begin{matrix}{{\frac{\beta}{\lambda_{3} + \beta}{\nabla S}},} & {M = 0} \\{{\nabla S},} & {{M \neq 0},{{\nabla S^{2}} \geq \frac{\lambda_{2}}{\beta}}} \\{0,} & \;\end{matrix} \right.} & \left( {{Formula}\mspace{14mu} 8} \right)\end{matrix}$

Solution of the variable w:

$\begin{matrix}{{\min\limits_{w}{\lambda_{1}{w}^{0.5}}} + {\gamma{{w - {\nabla S}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 9} \right)\end{matrix}$

We solve the Formula 9 with relatively total variation (RTV);

The solution of a significant structure variable S of the blurred imageis as follows:

$\begin{matrix}{{\min\limits_{s}{{{S \otimes k} - L}}^{2}} + {\lambda_{1}{w}^{0.5}} + {\beta{{u - {\nabla S}}}_{2}^{2}} + {\gamma{{w - {\nabla S}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 10} \right)\end{matrix}$

Based on Parseval's theorem, S is obtained by Fourier transform ofFormula 10:

$\begin{matrix}{S = {\mathcal{F}^{- 1}\left( \frac{\begin{matrix}{{\mathcal{F}{(I) \circ {\overset{\_}{\mathcal{F}}(k)}}} -} \\{{{\beta\mathcal{F}}{(u) \circ \overset{\_}{\mathcal{F}}}(\nabla)} + {{{\gamma\mathcal{F}}(w)} \circ {\overset{\_}{\mathcal{F}}(\nabla)}}}\end{matrix}}{\begin{matrix}{{\mathcal{F}{(k) \circ {\overset{\_}{\mathcal{F}}(k)}}} +} \\{{{\beta\mathcal{F}}{(\nabla) \circ \overset{\_}{\mathcal{F}}}(\nabla)} + {{{\gamma\mathcal{F}}(\nabla)} \circ {\overset{\_}{\mathcal{F}}(\nabla)}}}\end{matrix}} \right)}} & \left( {{Formula}\mspace{14mu} 11} \right)\end{matrix}$

Wherein,

indicates the Fourier transform, and

⁻² indicates Fourier inversion.

2) A process of blurring kernel evaluation and outlier suppressionspecifically includes the following steps:

In the present invention, the blurring kernel is estimated with gradientinformation and the significant structure, and the blurring kerneltrajectory is obtained through iterative update of Formula 14 andFormula 15, as shown in FIG. 6, diagram on the right of FIG. 8 and FIG.9(c).

Specifically, the blurring kernel is estimated with the significantstructure S of the evaluated blurring image in the present invention. Wesuppress the outlier in the blurring kernel with L0 norm, and theoptimization process is as follows:

$\begin{matrix}{{{{\min\limits_{k}{{{{\nabla S} \otimes k} - I}}_{2}^{2}} + {\psi_{1}{k}_{2}^{2}} + {\psi_{2}{{\nabla k}}_{0}{s.t.\mspace{14mu} k}}} \geq 0},{{k}_{1} = 1}} & \left( {{Formula}\mspace{14mu} 12} \right)\end{matrix}$

Similarly, we introduce a substitution variable v for iterative update,and the variant of the Formula 12 is as follows:

$\begin{matrix}{{\min\limits_{v,k}{{{{\nabla S} \otimes k} - I}}_{2}^{2}} + {\psi_{1}{k}_{2}^{2}} + {\psi_{2}{v}_{0}} + {\varphi{{v - {\nabla k}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 13} \right)\end{matrix}$

The solutions of the two variables (v and k are as follows:

$\begin{matrix}{v = \left\{ \begin{matrix}{{\nabla k},} & {{\nabla k^{2}} \geq \frac{\psi_{2}}{\varphi}} \\{0,} & \;\end{matrix} \right.} & \left( {{Formula}\mspace{14mu} 14} \right) \\{k = {\mathcal{F}^{- 1}\left( \frac{{{\mathcal{F}\left( {\nabla I} \right)} \circ {\overset{\_}{\mathcal{F}}\left( {\nabla S} \right)}} + {{{\varphi\mathcal{F}}(v)} \circ {\overset{\_}{\mathcal{F}}(\nabla)}}}{{{\mathcal{F}\left( {\nabla S} \right)} \circ {\overset{\_}{\mathcal{F}}\left( {\nabla S} \right)}} + {{{\varphi\mathcal{F}}(\nabla)} \circ {\overset{\_}{\mathcal{F}}(\nabla)}}} \right)}} & \left( {{Formula}\mspace{14mu} 15} \right)\end{matrix}$

3) The restoration process of the blurred image specifically includesthe following steps:

Restoring the blurred image by using the estimated blurring kernel withthe non-blind deconvolution technology:

In the implementation of the present invention, the non-blinddeconvolution is realized with a Richardson-Lucy algorithm. SeeLiterature 1 (Perrone, Daniele, and Paolo Favaro. “Total variation blinddeconvolution: The devil is in the details.” Proceedings of the IEEEConference on Computer Vision and Pattern Recognition. 2014).

Compared with the prior art, the present invention has beneficialeffects:

The present invention proposes a priori constraint and outliersuppression based image deblurring method. The significant structure inthe blurred image is obtained by use of L0 norm constraint andheavy-tailed a priori information. Based on the significant structure,the L0 norm constraint is used to evaluate the blurring kernel. Theevaluated blurring kernel is subjected to outlier suppression. The finalrestored image is obtained by using a non-blind deconvolution algorithm.The present invention can solve the problems of the existing algorithms:a priori assumption is incorrect; a priori constraint is inappropriate;and the blurring kernel has outliers and the like. By solving theproblems, the present invention can prominently improve the restorationlevel of the blurred image.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow diagram of specific implementation of the presentinvention;

FIG. 2 is a flow block diagram of the method of the present invention;

Wherein, k^(n) indicates a blurring kernel obtained by evaluating animage with minimum size, and k⁰ indicates evaluated blurring kernelfinally obtained.

FIG. 3 is a texture diagram of a significant structure of a blurredimage in an embodiment of the present invention;

Wherein, (a) indicates an original blurred image; (b) indicates gradeddistribution of the original blurred image; (c) indicates distributionof a gradient histogram; and (d) indicates an energy diagram of r valueexpressed by color information, i.e., a value distribution diagram of anoriginal image r(x).

FIG. 4 is an exemplary diagram for the significant structure of theblurred image in the embodiment of the present invention.

FIG. 5 is significant structures of the blurred images with differentsizes in the embodiment of the present invention;

Wherein, (a)˜(d) indicate the blurred images with different sizes.

FIG. 6 is a blurring kernel obtained through iterative update of theembodiment of the present invention.

FIG. 7 is an image after restoring the blurred image of the embodimentof the present invention.

FIG. 8 is a comparison diagram by magnifying the blurred image andrestored image thereof in the embodiment of the present invention.

FIG. 9 is comparison of the blurred image, the significant structure andthe restored diagram in the embodiment of the present invention;

Wherein, Figure (a) indicates the original blurred image; Figure (b)indicates the significant structure; and Figure (c) indicates theblurred restored image.

DETAILED DESCRIPTION OF THE INVENTION

Further description is made as follows to the present invention throughan embodiment in combination with the drawings, but the range of thepresent invention is not limited in any way.

A priori constraint and outlier suppression based deblurring methodproposed by the present invention is shown in FIG. 2. In the Figure,k^(n) indicates a blurring kernel obtained by evaluating an image withminimum size, and k⁰ indicates evaluated blurring kernel finallyobtained. In the method of the present invention, the blurring kernel iscontinuously updated with several sampling ways, and the final restoredimage is obtained by using a non-blind deconvolution algorithm.

The method of the present invention includes the specific steps asfollows:

Table 1 is a description for names of parameters adopted in thefollowing steps and corresponding parameter meanings thereof

TABLE 1 Parameter List Parameter name Description λ1 Coefficient of asubstitution variable w in an evaluation process of a significantstructure S λ2 Coefficient of a texture region in the evaluation processof the significant structure S λ3 Coefficient of a smooth region in theevaluation process of the significant structure S ψ1 Weight of ablurring kernel k in an evaluation process of the blurring kernel ψ2Weight of a substitution variable v in the evaluation process of theblurring kernel γ Weight of iterative update in the evaluation processof the significant structure S β Weight of iterative update in theevaluation process of the significant structure S φ Weight of iterativeupdate in the evaluation process of the blurring kernel

Step 1. Selection of a blurring model: the present invention adopts amodel of Formula 1, and assumes that the noise follows Gaussiandistribution, and an optimized equation shown in Formula 2 is obtained;

In the present invention, a convolution model is used for fitting ablurring process of a clear image, as shown in the Formula 1:

I=L⊗k+η  (Formula 1)

wherein, I indicates a blurred image, k indicates a blurring kernel, andη indicates noise (assume the distribution thereof is Gaussian noise);

A priori constraint with a heavy-tailed effect is taken as distributionof a significant structure gradient of the blurred image, as shown inFormula 2:

$\begin{matrix}{{\min\limits_{s}{{{S \otimes k} - L}}^{2}} + {\lambda_{1}{{\nabla S}}^{0.5}}} & \left( {{Formula}\mspace{14mu} 2} \right)\end{matrix}$

Wherein, S indicates the significant structure of the blurred image;

Step 2: evaluation of the significant structure of the blurred image:

Firstly, obtaining texture calibration of the significant structure withFormula 4 and Formula 5, as shown in FIG. 3(b). FIG. 3 is a texturediagram of a significant structure of a blurred image in an embodiment,wherein, (a) indicates an original blurred image; (b) indicates gradeddistribution of the original blurred image; (c) indicates distributionof a gradient histogram; and (d) indicates a value distribution of theoriginal image r(x). The texture calibration of the significantstructure with the Formula 4 and the Formula 5 is specifically asfollows:

We introduce L0 norm to constrain texture of the significant structure Sof the blurred image, and meanwhile, limit noise of a smooth region in Swith L2 norm. The updated formula is shown in the Formula 3:

$\begin{matrix}{{\min\limits_{s}{{{S \otimes k} - L}}^{2}} + {\lambda_{1}{{\nabla S}}^{0.5}} + {\lambda_{2}{{{\nabla S} \circ M}}_{0}} + {\lambda_{3}{{{\nabla S} \circ \left( {1 - M} \right)}}_{2}^{2}}} & \left( {{Formula}\mspace{11mu} 3} \right)\end{matrix}$

Wherein, M indicates two-value calibration of the texture in thesignificant structure S of the blurred image, (1−M) indicates two-valuecalibration of the smooth region in S. We define M with the Formula 4and the Formula 5:

$\begin{matrix}{{r(x)} = \frac{{\sum\limits_{y \in {N_{h}{(x)}}}{\nabla{S(y)}}}}{{\sum\limits_{y \in {N_{h}{(x)}}}{{\nabla{S(y)}}}} + 0.5}} & \left( {{Formula}\mspace{14mu} 4} \right) \\{M = {H\left( {r - \tau_{r}} \right)}} & \left( {{Formula}\mspace{14mu} 5} \right)\end{matrix}$

In the Formula 4, x indicates a location of a pixel point, y indicates apixel point centering on the pixel point and having a window size withina range of N^(h), and r(x) indicates a degree that the pixel point atthe location x belongs to the texture part. The texture in S can bepreliminarily divided with the Formula 4, the value of r(x) is (0, 1),and r(x) is in proportion to the possibility that x belongs to thetexture part. Meanwhile, the Formula 4 also limits the appearance of amutational texture (when the size of the blurring kernel is greater thanthat of blurred image detail, the image restoration is failed,therefore, the mutational texture should be limited). M in the Formula 5is obtained by Heaviside step function, wherein τ_(r) indicates athreshold of r, which is used for distinguishing a texture region andthe smooth region in the significant structure S. In the presentinvention, we obtain τ_(r) with a histogram equalization method.

Secondly, obtaining the significant structure of the blurred image withFormulas 8, 9 and 11, as shown in FIG. 4. FIG. 5 is different structuresobtained by estimation at different sizes, specifically as follows:

We introduce two substitution variables u and w to selectivelysubstitute ∇S to obtain the Formula 3, and update S with an iterativemethod. A variant of the Formula 3 is as follows:

$\begin{matrix}{{\min\limits_{S,u,w}{{{S \otimes k} - L}}^{2}} + {\lambda_{1}{w}^{0.5}} + {\lambda_{2}{{u \circ M}}_{0}} + {\lambda_{3}{{u \circ \left( {1 - M} \right)}}_{2}^{2}} + {\beta{{u - {\nabla S}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 6} \right)\end{matrix}$

We obtain the solution of each iteration S, u and w with alternatelyupdated method; Solution of the variable u:

$\begin{matrix}{{\min\limits_{u}{\lambda_{2}{{u \circ M}}_{0}}} + {\lambda_{3}{{u \circ \left( {1 - M} \right)}}_{2}^{2}} + {\beta{{u - {\nabla S}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 7} \right) \\{u = \left\{ \begin{matrix}{{\frac{\beta}{\lambda_{3} + \beta}{\nabla S}},} & {M = 0} \\{{\nabla S},} & {{M \neq 0},{{\nabla S^{2}} \geq \frac{\lambda_{2}}{\beta}}} \\{0,} & \;\end{matrix} \right.} & \left( {{Formula}\mspace{14mu} 8} \right)\end{matrix}$

Solution of the variable w:

$\begin{matrix}{{\min\limits_{w}{\lambda_{1}{w}^{0.5}}} + {\gamma{{w - {\nabla S}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 9} \right)\end{matrix}$

We solve the Formula 9 with relatively total variation (RTV); Solutionof the variable S:

$\begin{matrix}{{\min\limits_{s}{{{S \otimes k} - L}}^{2}} + {\lambda_{1}{w}^{0.5}} + {\beta{{u - {\nabla S}}}_{2}^{2}} + {\gamma{{w - {\nabla S}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 10} \right)\end{matrix}$

Based on Parseval's theorem, we carry out Fourier transform on Formula10 to obtain S:

$\begin{matrix}{S = {\mathcal{F}^{- 1}\left( \frac{\begin{matrix}{{\mathcal{F}{(l) \circ \mathcal{F}}(k)} +} \\{{{\beta\mathcal{F}}{(u) \circ \overset{\_}{\mathcal{F}}}(\nabla)} + {{{\gamma\mathcal{F}}(w)} \circ {\overset{\_}{\mathcal{F}}(\nabla)}}}\end{matrix}}{\begin{matrix}{{\mathcal{F}{(k) \circ \overset{\_}{\mathcal{F}}}(k)} +} \\{{{\beta\mathcal{F}}{(\nabla) \circ \overset{\_}{\mathcal{F}}}(\nabla)} + {{{\gamma\mathcal{F}}(\nabla)} \circ {\overset{\_}{\mathcal{F}}(\nabla)}}}\end{matrix}} \right)}} & \left( {{Formula}\mspace{14mu} 11} \right)\end{matrix}$

Wherein,

indicates the Fourier transform, and

⁻² indicates Fourier inversion.

Step 3. blurring kernel estimation, specifically as follows:

In the present invention, the blurring kernel is estimated with gradientinformation and the significant structure, and the blurring kerneltrajectory is obtained through iterative update of Formula 14 andFormula 15, as shown in FIG. 6, diagram on the right of FIG. 8 and FIG.9(c).

Specifically, the blurring kernel is estimated with the significantstructure S of the evaluated blurring image in the present invention. Wesuppress the outlier in the blurring kernel with L0 norm, and theoptimization process is as follows:

$\begin{matrix}{{{\min\limits_{k}{{{{\nabla S} \otimes k} - {\nabla I}}}_{2}^{2}} + {\psi_{1}{k}_{2}^{2}} + {\psi_{2}{{\nabla k}}_{0}}}{{{s.t.\mspace{14mu} k} \geq 0},\text{}{{k}_{1} = 1}}} & \left( {{Formula}\mspace{14mu} 12} \right)\end{matrix}$

Similarly, we introduce a substitution variable v for iterative update,and the variant of the Formula 12 is as follows:

$\begin{matrix}{{\min\limits_{v,k}{{{{\nabla S} \otimes k} - {\nabla I}}}_{2}^{2}} + {\psi_{1}{k}_{2}^{2}} + {\psi_{2}{v}_{0}} + {\varphi{{v - {\nabla k}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 13} \right)\end{matrix}$

The solutions of the two variables (v and k) are as follows:

$\begin{matrix}{v = \left\{ \begin{matrix}{{\nabla k},} & {{\nabla k^{2}} \geq \frac{\psi_{2}}{\varphi}} \\{0,} & {Others}\end{matrix} \right.} & \left( {{Formula}\mspace{14mu} 14} \right) \\{k = {\mathcal{F}^{- 1}\left( \frac{{{\mathcal{F}\left( {\nabla I} \right)} \circ {\overset{\_}{\mathcal{F}}\left( {\nabla S} \right)}} + {{{\varphi\mathcal{F}}(v)} \circ {\overset{\_}{\mathcal{F}}(\nabla)}}}{{{\mathcal{F}\left( {\nabla S} \right)} \circ {\overset{\_}{\mathcal{F}}\left( {\nabla S} \right)}} + {{{\varphi\mathcal{F}}(\nabla)} \circ {\overset{\_}{\mathcal{F}}(\nabla)}}} \right)}} & \left( {{Formula}\mspace{14mu} 15} \right)\end{matrix}$

Step 4: non-blind deconvolution, specifically as follows:

Any existing non-blind deconvolution algorithm can be adopted here.

The steps above can be expressed as the following algorithm flow:

Algorithm: a priori constraint and outlier suppression based imagedeblurring method Input: blurred image I Output: blurred kernel k, andblurred restored image L Start: Conducting down-sampling I⁽⁰⁾→I⁽¹⁾, . .. , I^((n)) to the blurred image (wherein I^((n)) has minimum size);Initializing the blurring kernel corresponding to the blurred image withthe minimum size; Iteration: Updating the blurred image I^((n)) →S;Iteration: Estimation of a significant structure: Using Formula 8 tosolve u; Using Formula 9 to solve w Using Formula 11 to solve thesignificant structure S; Estimation of the blurring kernel: UsingFormula 14 to solve v; Using Formula 15 to solve k; Stopping after theiterations reach 6; n−1→n; Stopping until n = 0; Using non-blinddeconvolution algorithm to obtain a restored image L.

In the implementation of the present invention, non-blind deconvolutionis carried out by using algorithm proposed in Literature 1 (Perrone,Daniele, and Paolo Favaro. “Total variation blind deconvolution: Thedevil is in the details.”Proceedings of the IEEE Conference on ComputerVision and Pattern Recognition. 2014). FIG. 7 is the restored image ofthe blurred image. Taking FIG. 8 for example additionally, the leftfigure is the blurred image and a magnifying region thereof, and theright figure is a restoration effect and corresponding magnifyingregion. Wherein the blurring kernel is expressed at the upper leftcorner of the right figure in a form of the energy diagram.

It should be noted that, the publicity of the embodiment aims at helpingfurther understand the present invention, but those skilled in the artcan understand that: all kinds of replacements and modifications may bepossible without departing from the spirit and range of the presentinvention and claims attached. Therefore, the present invention shouldnot be limited to the content disclosed by the embodiment, and the rangeprotected as required by the present invention is subject to the rangedefined by the claims.

1. A priori constraint and outlier suppression based image deblurringmethod, using a convolution model for fitting a blurring process of aclear image and restoring a blurred image I to achieve a purpose ofimage deblurring, comprising an evaluation process of a significantstructure of a blurred image, a process of blurring kernel estimationand outlier suppression, and a restoration process of a non-blinddeconvolution blurred image; 1) an evaluation process of the significantstructure of the blurred image I comprising the following steps: 11)taking a priori constraint with a heavy-tailed effect as distribution ofa significant structure gradient of the blurred image, as shown inFormula 2: $\begin{matrix}{{\min\limits_{s}{{{S \otimes k} - L}}^{2}} + {\lambda_{1}{{\nabla S}}^{0.5}}} & \left( {{Formula}\mspace{14mu} 2} \right)\end{matrix}$ wherein S indicates the significant structure of theblurred image (not image to be restored), and is used for evaluating theblurred kernel k in auxiliary manner; the first item of the Formula 2can be taken as a loss function; and the second item of the Formula 2simulates the heavy-tailed effect with Hyper-Laplacian; 12) evaluatingthe significant structure of the blurred image: introducing L0 norm toconstrain a texture of the significant structure S of the blurred image,and meanwhile, limiting noise of a smooth region in S with L2 norm. Theupdated formula is shown in Formula 3: $\begin{matrix}{{\min\limits_{s}{{{S \otimes k} - L}}^{2}} + {\lambda_{1}{{\nabla S}}^{0.5}} + {\lambda_{2}{{{\nabla S} \circ M}}_{0}} + {\lambda_{3}{{{\nabla S} \circ \left( {1 - M} \right)}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 3} \right)\end{matrix}$ wherein M indicates two-value calibration of the texturein the significant structure S of the blurred image, (1−M) indicatestwo-value calibration of the smooth region in S; and the third item inthe formula 3 constrains the details of a large size, and the last itemconstrains the smoothness; 13) solving the significant structure of theblurred image, specifically as follows: introducing two substitutionvariables u and w to selectively substitute ∇S to solve the Formula 3,wherein a variant of the Formula 3 is as follows: $\begin{matrix}{{\min\limits_{S,u,w}{{{S \otimes k} - L}}^{2}} + {\lambda_{1}{w}^{0.5}} + {\lambda_{2}{{u \circ M}}_{0}} + {\lambda_{3}{{u \circ \left( {1 - M} \right)}}_{2}^{2}} + {\beta{{u - {\nabla S}}}_{2}^{2}} + {\gamma{{w - {\nabla S}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 6} \right)\end{matrix}$ obtaining the solution of each iteration S, u and w withalternately updated method; and obtaining the significant structure S ofthe blurred image by Fourier transform and then updating; 2) a processof blurring kernel evaluation and outlier suppression: estimating theblurring kernel k with gradient information and the significantstructure S, and obtaining the blurring kernel trajectory throughiterative update and evaluation; and 3) the restoration process of theblurred image: restoring the blurred image by using the estimatedblurring kernel with the non-blind deconvolution technology.
 2. Theimage deblurring method of claim 1, wherein in step 12), two-valuecalibration M of the texture in the significant structure S is definedwith Formula 4 and Formula 5: $\begin{matrix}{{r(x)} = \frac{{\sum\limits_{y \in {N_{h}{(x)}}}{\nabla{S(y)}}}}{{\sum\limits_{y \in {N_{h}{(x)}}}{{\nabla{S(y)}}}} + 0.5}} & \left( {{Formula}\mspace{14mu} 4} \right) \\{M = {H\left( {r - \tau_{r}} \right)}} & \left( {{Formula}\mspace{14mu} 5} \right)\end{matrix}$ in the Formula 4, x indicates a location of a pixel point,y indicates a pixel point centering on the pixel point and having awindow size within a range of N_(h), and r(x) indicates a degree thatthe pixel point at the location x belongs to the texture part; thetexture in S can be preliminarily divided with the Formula 4, the valueof r(x) is (0, 1), and r(x) is in proportion to the possibility that xbelongs to the texture part; meanwhile, the Formula 4 also limits theappearance of a mutational texture; M in the Formula 5 is obtained byHeaviside step function, wherein τ_(r) indicates a threshold of r fordistinguishing a texture region and the smooth region in the significantstructure S.
 3. The image deblurring method of claim 2, wherein τ_(r) isobtained with a histogram equalization method.
 4. The image deblurringmethod of claim 1, wherein in step 13), S is updated with an iterativemethod; and solution of the variable u is as follows: $\begin{matrix}{{\min\limits_{u}{\lambda_{2}{{u \circ M}}_{0}}} + {\lambda_{3}{{u \circ \left( {1 - M} \right)}}_{2}^{2}} + {\beta{{u - {\nabla S}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 7} \right) \\{u = \left\{ \begin{matrix}{{\frac{\beta}{\lambda_{3} + \beta}{\nabla S}},} & {M = 0} \\{{\nabla S},} & {{M \neq 0},{{\nabla S^{2}} \geq \frac{\lambda_{2}}{\beta}}} \\{0,} & \;\end{matrix} \right.} & \left( {{Formula}\mspace{14mu} 8} \right)\end{matrix}$ solution of the variable w is as follows: $\begin{matrix}{{\min\limits_{w}{\lambda_{1}{w}^{0.5}}} + {\gamma{{w - {\nabla S}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 9} \right)\end{matrix}$ the Formula 9 is solved with relatively total variation(RTV); the solution of the variable S is as follows: $\begin{matrix}{{\min\limits_{s}{{{S \otimes k} - L}}^{2}} + {\lambda_{1}{w}^{0.5}} + {\beta{{u - {\nabla S}}}_{2}^{2}} + {\gamma{{w - {\nabla S}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 10} \right)\end{matrix}$ based on Parseval's theorem, S is obtained by Fouriertransform of Formula 10: $\begin{matrix}{S = {\mathcal{F}^{- 1}\left( \frac{\begin{matrix}{{\mathcal{F}{(l) \circ \mathcal{F}}(k)} +} \\{{{\beta\mathcal{F}}{(u) \circ \overset{\_}{\mathcal{F}}}(\nabla)} + {{{\gamma\mathcal{F}}(w)} \circ {\overset{\_}{\mathcal{F}}(\nabla)}}}\end{matrix}}{\begin{matrix}{{\mathcal{F}{(k) \circ \overset{\_}{\mathcal{F}}}(k)} +} \\{{{\beta\mathcal{F}}{(\nabla) \circ \overset{\_}{\mathcal{F}}}(\nabla)} + {{{\gamma\mathcal{F}}(\nabla)} \circ {\overset{\_}{\mathcal{F}}(\nabla)}}}\end{matrix}} \right)}} & \left( {{Formula}\mspace{14mu} 11} \right)\end{matrix}$ in the formula 11,

indicates the Fourier transform, and

⁻¹ indicates Fourier inversion.
 5. The image deblurring method of claim1, wherein in the step 2), the blurring kernel k is estimated with theestimated significant structure S of the blurred image, the outlier inthe blurring kernel is suppressed with L0 norm, and the optimizationprocess is shown by Formula 12: $\begin{matrix}{{{\min\limits_{k}{{{{\nabla S} \otimes k} - {\nabla I}}}_{2}^{2}} + {\psi_{1}{k}_{2}^{2}} + {\psi_{2}{{\nabla k}}_{0}}}{{{s.t.\mspace{14mu} k} \geq 0},\text{}{{k}_{1} = 1}}} & \left( {{Formula}\mspace{14mu} 12} \right)\end{matrix}$ a substitution variable v is introduced for iterativeupdate, and the variant of the Formula 12 is as follows: $\begin{matrix}{{\min\limits_{v,k}{{{{\nabla S} \otimes k} - {\nabla I}}}_{2}^{2}} + {\psi_{1}{k}_{2}^{2}} + {\psi_{2}{v}_{0}} + {\varphi{{v - {\nabla k}}}_{2}^{2}}} & \left( {{Formula}\mspace{14mu} 13} \right)\end{matrix}$ the two variables v and k are solved through Formulas 14and 15: $\begin{matrix}{v = \left\{ \begin{matrix}{{\nabla k},} & {{\nabla k^{2}} \geq \frac{\psi_{2}}{\varphi}} \\{0,} & \;\end{matrix} \right.} & \left( {{Formula}\mspace{14mu} 14} \right) \\{k = {\mathcal{F}^{- 1}\left( \frac{{{\mathcal{F}\left( {\nabla I} \right)} \circ {\overset{\_}{\mathcal{F}}\left( {\nabla S} \right)}} + {{{\varphi\mathcal{F}}(v)} \circ {\overset{\_}{\mathcal{F}}(\nabla)}}}{{{\mathcal{F}\left( {\nabla S} \right)} \circ {\overset{\_}{\mathcal{F}}\left( {\nabla S} \right)}} + {{{\varphi\mathcal{F}}(\nabla)} \circ {\overset{\_}{\mathcal{F}}(\nabla)}}} \right)}} & \left( {{Formula}\mspace{14mu} 15} \right)\end{matrix}$ wherein

indicates the Fourier transform, and

⁻¹ indicates Fourier inversion.
 6. The image deblurring method of claim1, wherein in the step 3), the non-blind deconvolution is realized witha Richardson-Lucy algorithm.
 7. The image deblurring method of claim 1,wherein a blurring process of a clear image is fitted by using theconvolution model in Formula 1:I=L⊗k+η  (Formula 1) wherein I indicates the blurred image, k indicatesthe blurring kernel, and η indicates the noise.
 8. The image deblurringmethod of claim 7, wherein the distribution of the noise η is Gaussiandistribution.